Question

Which of the following statement is wrong? (1) An electron revolving in the level \(n=1\) has less energy than that revolving in the level \(n=2\). (2) The energy of electrons in the \(s, p, d\) and \(f\) sublevels in the same shell varies in the order \(s>p>d>f\) (3) Any electron can jump from an inner level to an outer level by absorbing energy. (4) An atom is stable in ground state than in one of its excited state.

Short answer

Statement 2 is wrong.

Step-by-step solution

Analyze Statement 1

Determine if an electron in level \(n=1\) has less energy than in level \(n=2\). In atomic structure, the energy of electrons increases as the principal quantum number \(n\) increases. Thus, an electron in level \(n=1\) should have less energy than in level \(n=2\). This statement is correct.

Analyze Statement 2

Evaluate the energy levels of \(s, p, d\), and \(f\) sublevels within the same principal quantum number shell. The energy order for these sublevels within the same shell actually follows \(s < p < d < f\). Therefore, this statement is incorrect because it states the opposite order.

Analyze Statement 3

Consider whether an electron can jump from an inner level to an outer level by absorbing energy. This is true, as electrons can move to higher energy levels by absorbing photons or energy. Thus, this statement is correct.

Analyze Statement 4

Determine if an atom is more stable in its ground state compared to an excited state. Atoms are indeed more stable in their ground state because the ground state is the lowest energy state. Therefore, this statement is correct.

Key concepts

Energy Levels

In atomic structure, energy levels refer to the specific energies that electrons can have while orbiting the nucleus of an atom. These levels are quantized, meaning electrons can only exist at set energy levels, not between them. The first energy level, designated as n=1, is the closest to the nucleus and has the lowest energy. As you move to higher principal quantum numbers (like n=2, n=3, etc.), the energy increases. This is why an electron in the level n=1 has less energy than one in the level n=2. The energy levels get closer together as you move farther from the nucleus, and in theory, they converge at an infinite distance. Therefore, higher energy levels are not as distinct as those closer to the nucleus. Each energy level can also be divided into sublevels or subshells (s, p, d, f), which further classify the electron distribution.

Principal Quantum Number

The principal quantum number, symbolized as 'n', is essential in describing the atomic structure. It defines the main energy level or shell that an electron occupies. The principal quantum number is always a positive integer (1, 2, 3, etc.). As 'n' increases, the average distance of the electron from the nucleus and the electron's energy also increase. The principal quantum number also indirectly determines the number of sublevels or orbitals contained within that energy level: when n=1, there is only one sublevel (s); when n=2, there are two sublevels (s and p); when n=3, there are three sublevels (s, p, and d); and so forth. Higher principal quantum numbers can hold more electrons, following the pattern: each energy level can contain a maximum of 2n^2 electrons.

Electron Transitions

Electron transitions describe how electrons jump between energy levels within an atom. These transitions occur when an electron absorbs or releases energy. When an electron absorbs energy, it jumps from a lower energy level to a higher one, called an excited state. Conversely, when an electron releases energy, it falls from a higher energy level back down to a lower one. For instance, if an electron falls back to its original lower energy level, the atom releases energy in the form of light. This principle is behind the operation of many light-emitting devices like LEDs. The energy difference between the levels dictates the wavelength—or color—of the light emitted. Electron transitions are responsible for atomic spectra, which can be unique for each element and serve as a fingerprint to identify them.

Ground State vs Excited State

An atom's ground state is its lowest energy state, where all electrons are in their lowest possible energy levels. This state is the most stable configuration for an atom because it has minimal energy. In contrast, an excited state occurs when one or more electrons absorb energy and move to higher energy levels. While in an excited state, the atom is less stable and will eventually release the absorbed energy to return to the ground state. This released energy often appears as light or other electromagnetic radiation. The ground state is preferred because it represents a balance where the electrons are as close to the nucleus as possible, minimizing the atom's overall potential energy. Excited states, being temporary and higher in energy, are naturally rare and usually revert to the ground state quickly.